how to find the height of a trapezoid with median 12 and area 84

Question

An illustrative image showing the processes which can be used in solving a mathematical problem. The focus should be on a trapezoid, with its median (the line segment connecting the midpoints of its non-parallel sides) clearly marked and its area colored differently. The trapezoid's median should be represented with a length of 12 units and the area of the trapezoid should depict an area equivalent to 84 square units. This image should not contain any text. Please add elements like a ruler or a protractor as additional tools helpful in deriving measurements, to display the process of solving geometric problems.

how to find the height of a trapezoid with median 12 and area 84

Answer 1

A=1/2(h)(a+b)

84=1/2(h)(24)
84=12(h)
h=7

Answer 2

h = height

84 = 12h
84/12 = h

Answer 3

Why did the trapezoid go to therapy? It had trouble finding its height! But don't you worry, I'm here to help.

To find the height of a trapezoid, you first need to know the lengths of its bases. Unfortunately, you only provided the median and area. Are you sure you're not confusing trapezoids with therapists? 😄

Answer 4

To find the height of a trapezoid with a given median and area, you can follow these steps:

Step 1: Recall the formula to find the area of a trapezoid, which is given by the equation:

Area = (1/2) * (sum of bases) * height

Step 2: Substitute the given values into the equation. Let's call the upper base of the trapezoid "a," the lower base "b," and the height "h." The median of a trapezoid is the average of its bases, so in this case, the median is equal to (a + b) / 2. Also, the given area is 84.

We can rewrite the formula as:

84 = (1/2) * (a + b) * h

Step 3: Since the median is given as 12 and is equal to (a + b) / 2, we can substitute 12 for (a + b) / 2:

84 = (1/2) * 12 * h

Simplify the equation:

84 = 6h

Step 4: Solve for h by dividing both sides of the equation by 6:

h = 84 / 6

Simplify further:

h = 14

Therefore, the height of the trapezoid is 14 units.

Answer 5

To find the height of a trapezoid with the median and area given, you can use the formula:

Area = (1/2) * height * (base1 + base2)

In this case, the area is given as 84 and the median is given as 12. Let's label the bases as base1 and base2.

We know that the median of a trapezoid is the average of the two bases. So, we have:

median = (base1 + base2) / 2

Substituting the given median value of 12 into the equation, we get:

12 = (base1 + base2) / 2

Next, we can simplify the formula for the area by substituting the given values of the area (84) and the median (12):

84 = (1/2) * height * (base1 + base2)

Now, let's solve the two equations simultaneously to find the values of base1 and base2. From the first equation, base1 + base2 = 24. We can solve for base1 or base2 by isolating one variable. Let's isolate base1:

base1 = 24 - base2

Substituting this value for base1 in the second equation, we have:

84 = (1/2) * height * (24 - base2 + base2)

Simplifying further:

84 = (1/2) * height * 24

Now, multiply both sides of the equation by 2:

168 = height * 24

Divide both sides by 24:

height = 168 / 24

Finally, calculate the height:

height = 7

Therefore, the height of the trapezoid is 7 units.